<p>Interrupted time series (ITS) models play an important role in directing research on the effects of planned or unexpected interventions on data analysis. The ITS analysis is an increasingly popular technique for evaluating public health interventions, their effects on diseases, and their capacity to make flexible predictions about various consequences. Hence, the first-order interrupted autoregressive model is proposed with the autocorrelated skew-Normal innovation. This is motivated by the issue of identifying a potential probabilistic model for the nonlinear time series with intervention for clinical data sets. By classifying before and after the intervention stages and examining changes during the intervention, the analysis attentively estimates the effects of the intervention. The ECME algorithm for iteratively estimating the parameters is described, and the observed information matrix is derived analytically. A preferred aspect of the data analysis is the evaluation of robustness of estimates in statistical models and the local impact of small perturbations. Therefore, the local influence analysis of the considered model is thoroughly examined while taking into account three perturbations. To evaluate the performance of proposed methods, some simulation data sets considering the ECME estimates are presented to show the robustness of estimates against influential observations. Finally, the proposed process is executed favorably to model the new cases of COVID-19 time series in the Czech Republic, with some goodness of fit benchmarks, allowing for both the applicability of the proposed process and the influence of diagnostic analysis.</p>